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Math Help - Mean & Variance Problem... (Any hints or help will do)

  1. #1
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    Mean & Variance Problem... (Any hints or help will do)

    X1and X2 are independently distributed random variables with
    P(X1 = Z+1 ) = P(X1 = Z-1 ) = 1/2
    P(X2 = Z-2 ) = P(X2 = Z+2 ) = 1/2.
    Find the value of a and b which minimize the variance of Y = aX1 + bX2 subject to the condition that E[Y] = Z.
    What is the minimum value of this variance?
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  2. #2
    MHF Contributor matheagle's Avatar
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    V(X1)=1 and V(X2)=4

    The constraint since E(X1)=z=E(X2) is a+b=1, where z should be lower case, not upper case.

    So use calc 1 to minimize a^2 +4b^2 given a+b=1, by inserting one of these two variables,a,b.

    You could use LaGrange, but cal 1 is easier.

    I get a=4/5, b=1/5 giving me 20/25=.8 as the answer.
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